Polarized neutron diffraction experiments conducted at 4.2 K on Cs3CoCl5 crystals are analyzed by using a 4-dimensional model Hilbert space made of ab initio n-electron wave functions of the CoCl42- molecular ion. The magnetic structure factors given by the best ensemble density operator that is representable in our model space are fitted to the experimental ones by optimizing two spin-orbit mixing coefficients of the embedded CoCl42- ions and several configuration interaction coefficients. The optimized density operator can in turn be used to calculate any observable. Here we present density maps of the spin density, and the orbital current density. The method, which is general, gives a goodness of fit, chi(2), less than 1 with fewer parameters optimized than other methods employed so far. It provides a new way of gaining information about spin-orbit coupling and the relative contributions of spin and orbital motion to the magnetic properties of an atomic or molecular system. Another interesting finding is that a chi(2) less than 1, can be obtained with a spin density of the same sign everywhere in space, leading to the conclusion that spin polarization is within the experimental error. The so-called "collinear approximation" has been avoided in this work although it has been found to be justified for this system. A direct comparison is made between calculated and experimental flipping ratios.